For $t \geq 0$, a particle moves along the $x$-axis. The velocity of the particle at time $t$ is given by $v ( t ) = 1 + 2 \sin \left( \frac { t ^ { 2 } } { 2 } \right)$. The particle is at position $x = 2$ at time $t = 4$. (a) At time $t = 4$, is the particle speeding up or slowing down? (b) Find all times $t$ in the interval $0 < t < 3$ when the particle changes direction. Justify your answer. (c) Find the position of the particle at time $t = 0$. (d) Find the total distance the particle travels from time $t = 0$ to time $t = 3$.
For $t \geq 0$, a particle moves along the $x$-axis. The velocity of the particle at time $t$ is given by $v ( t ) = 1 + 2 \sin \left( \frac { t ^ { 2 } } { 2 } \right)$. The particle is at position $x = 2$ at time $t = 4$.\\
(a) At time $t = 4$, is the particle speeding up or slowing down?\\
(b) Find all times $t$ in the interval $0 < t < 3$ when the particle changes direction. Justify your answer.\\
(c) Find the position of the particle at time $t = 0$.\\
(d) Find the total distance the particle travels from time $t = 0$ to time $t = 3$.